Thomas A Gerds

University of Copenhagen, København, Capital Region, Denmark

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Publications (98)263.67 Total impact

  • Thomas A. Gerds, Jørgen Hilden
    Statistics in Medicine 08/2014; 33(19). · 2.04 Impact Factor
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    ABSTRACT: We introduce a new approach to competing risks using random forests. Our method is fully non-parametric and can be used for selecting event-specific variables and for estimating the cumulative incidence function. We show that the method is highly effective for both prediction and variable selection in high-dimensional problems and in settings such as HIV/AIDS that involve many competing risks.
    Biostatistics 04/2014; · 2.43 Impact Factor
  • Thomas A Gerds, Per K Andersen, Michael W Kattan
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    ABSTRACT: A predicted risk of 17% can be called reliable if it can be expected that the event will occur to about 17 of 100 patients who all received a predicted risk of 17%. Statistical models can predict the absolute risk of an event such as cardiovascular death in the presence of competing risks such as death due to other causes. For personalized medicine and patient counseling, it is necessary to check that the model is calibrated in the sense that it provides reliable predictions for all subjects. There are three often encountered practical problems when the aim is to display or test if a risk prediction model is well calibrated. The first is lack of independent validation data, the second is right censoring, and the third is that when the risk scale is continuous, the estimation problem is as difficult as density estimation. To deal with these problems, we propose to estimate calibration curves for competing risks models based on jackknife pseudo-values that are combined with a nearest neighborhood smoother and a cross-validation approach to deal with all three problems. Copyright © 2014 John Wiley & Sons, Ltd.
    Statistics in Medicine 03/2014; · 2.04 Impact Factor
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    ABSTRACT: Using a large, contemporary primary care population we aimed to provide absolute long-term risks of cardiovascular death (CVD) based on the QTc interval and to test whether the QTc interval is of value in risk prediction of CVD on an individual level. Digital electrocardiograms from 173 529 primary care patients aged 50-90 years were collected during 2001-11. The Framingham formula was used for heart rate-correction of the QT interval. Data on medication, comorbidity, and outcomes were retrieved from administrative registries. During a median follow-up period of 6.1 years, 6647 persons died from cardiovascular causes. Long-term risks of CVD were estimated for subgroups defined by age, gender, cardiovascular disease, and QTc interval categories. In general, we observed an increased risk of CVD for both very short and long QTc intervals. Prolongation of the QTc interval resulted in the worst prognosis for men whereas in women, a very short QTc interval was equivalent in risk to a borderline prolonged QTc interval. The effect of the QTc interval on the absolute risk of CVD was most pronounced in the elderly and in those with cardiovascular disease whereas the effect was negligible for middle-aged women without cardiovascular disease. The most important improvement in prediction accuracy was noted for women aged 70-90 years. In this subgroup, a total of 9.5% were reclassified (7.2% more accurately vs. 2.3% more inaccurately) within clinically relevant 5-year risk groups when the QTc interval was added to a conventional risk model for CVD. Important differences were observed across subgroups when the absolute long-term risk of CVD was estimated based on QTc interval duration. The accuracy of the personalized CVD prognosis can be improved when the QTc interval is introduced to a conventional risk model for CVD.
    European Heart Journal 03/2014; · 14.72 Impact Factor
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    ABSTRACT: The concordance probability is a widely used measure to assess discrimination of prognostic models with binary and survival endpoints. We formally define the concordance probability for a prognostic model of the absolute risk of an event of interest in the presence of competing risks and relate it to recently proposed time-dependent area under the receiver operating characteristic curve measures. For right-censored data, we investigate inverse probability of censoring weighted (IPCW) estimates of a truncated concordance index based on a working model for the censoring distribution. We demonstrate consistency and asymptotic normality of the IPCW estimate if the working model is correctly specified and derive an explicit formula for the asymptotic variance under independent censoring. The small sample properties of the estimator are assessed in a simulation study also against misspecification of the working model. We further illustrate the methods by computing the concordance probability for a prognostic model of coronary heart disease (CHD) events in the presence of the competing risk of non-CHD death.
    Biostatistics 02/2014; · 2.43 Impact Factor
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    ABSTRACT: Background Compelling biomarkers identifying prostate cancer patients with a high risk of progression during active surveillance (AS) are needed. Objective To examine the association between ERG expression at diagnosis and the risk of progression during AS. Design, setting, and participants This study included 265 patients followed on AS with prostate-specific antigen (PSA) measurements, clinical examinations, and 10–12 core rebiopsies from 2002 to 2012 in a prospectively maintained database. ERG immunohistochemical staining was performed on diagnostic paraffin-embedded formalin-fixed sections with a ready-to-use kit (anti-ERG, EPR3864). Men were characterised as ERG positive if a minimum of one tumour focus demonstrated ERG expression. Outcome measurements and statistical analysis Overall AS progression was defined as clinical progression: increased clinical tumour category ≥cT2b by digital rectal examination and ultrasound, and/or histopathologic progression: upgrade of Gleason score, more than three positive cores or bilateral positive cores, and/or PSA progression: PSA doubling time <3 yr. Risk of progression was analysed using multiple cause-specific Cox regression and stratified cumulative incidences (Aalen-Johansen method). Curatively intended treatment, watchful waiting, and death without progression were treated as competing events. Results and limitations A total of 121 of 142 ERG-negative and 96 of 123 ERG-positive patients had complete diagnostic information. In competing risk models, the ERG-positive group showed significantly higher incidences of overall AS progression (p < 0.0001) and of the subgroups PSA progression (p < 0.0001) and histopathologic progression (p < 0.0001). The 2-yr cumulative incidence of overall AS progression was 21.7% (95% confidence interval [CI], 14.3–29.1) in the ERG-negative group compared with 58.6% (95% CI, 48.7–68.5) in the ERG-positive group. ERG positivity was a significant predictor of overall AS progression in multiple Cox regression (hazard ratio: 2.45; 95% CI, 1.62–3.72; p < 0.0001). The main limitation of this study is its observational nature. Conclusions In our study, ERG positivity at diagnosis can be used to estimate the risk of progression during AS. If confirmed, ERG status can be used to individualise AS programmes. Patient summary The tissue biomarker ERG identifies active surveillance patients with an increased risk of disease progression.
    European Urology 01/2014; · 10.48 Impact Factor
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    ABSTRACT: The case-time-control design is an extension of the case-crossover design capable of handling time trends in the exposure of the general population. Time-invariant confounders are controlled for by the design itself. The idea is to compare the exposure status of a person in one or several reference periods during which no event occurred with the exposure status of the same person in the index period where the event occurred. By comparing case-crossover results in cases to case-crossover results in controls, the exposure-outcome association can be estimated by conditional logistic regression. We review the mathematical assumptions underlying the case-time-control design and examine sensitivity to deviations from the assumed independence of within-individual exposure history. Results from simulating various scenarios suggest that the design is quite robust to deviations from this model assumption. In addition, we show that changes in exposure probability over time can be modeled in a flexible way using splines.
    Epidemiology (Cambridge, Mass.) 11/2013; · 5.51 Impact Factor
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    ABSTRACT: Pregnant women are at an increased risk of venous thromboembolism (VTE). Risk factors for VTE among pregnant women are not sufficiently investigated. To examine pharmacological and non-pharmacological VTE risk factors during pregnancy (antepartum). The population comprised all pregnant women in Denmark aged 15-50 giving birth 2003-2010. Pregnancies were linked on an individual level with national registers for hospital admissions and drug dispenses from pharmacies. Risk of first occurring VTE antepartum was examined with Cox regression models. Out of 299 810 pregnancies, 337 experienced a VTE, incidence rate 1.1 (95% confidence interval [CI] 1.0-1.3) per 1000 pregnancies. Being underweight (body mass index [BMI] < 18.5 kg/m(2) ) was associated with a decreased risk of VTE (hazard ratio [HR] 0.53 [CI 0.29-0.98]) compared to normal weight (18.5 ≤ BMI < 25 kg/m(2) ). Overweight (25 ≤ BMI < 30 kg/m(2) ) increased VTE risk (HR 1.30 [CI 1.01-1.67]) but obesity (BMI ≥ 30 kg/m(2) ) was insignificant (HR 1.14 [CI 0.82-1.58]). A history of VTE was highly significant (HR 72.65 [CI 51.17-103.15]). The youngest (<20 years) and oldest (≥35 years) had insignificantly increased risks (HR 1.45 [CI 0.80-2.62] and HR 1.31 [CI 0.98-1.75], respectively) compared to those aged 20-30 years. Sixteen groups of medications, including anti-infectious medications, hormones, aminosalicylic acid, insulin, and benzodiazepine derivatives, were associated with VTE. The risk of antepartum VTE was increased in women with prior VTE. Compared to normal weight women, being underweight decreased the risk of VTE whereas being overweight increased the risk. Also, the use of several medications was associated with increased risk of VTE. Copyright © 2013 John Wiley & Sons, Ltd.
    Pharmacoepidemiology and Drug Safety 10/2013; · 2.90 Impact Factor
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    ABSTRACT: Preeclampsia may affect severely the cerebral circulation leading to impairment of cerebral autoregulation, edema, and ischemia. It is not known whether impaired autoregulation occurs before the clinical onset of preeclampsia, and whether this can predict the occurrence of preeclampsia. Seventy-two women at 25 to 28 weeks of gestation were studied. Control values were derived from 26 nonpregnant women. Dynamic properties of cerebral autoregulation (DCA) were measured in the middle and posterior cerebral artery using transcranial Doppler and transfer function analysis (phase and gain) of respiratory-induced 0.1 Hz hemodynamic oscillations. Uterine artery ultrasound was performed to search for a notch sign as an early marker of general endothelial dysfunction. All women were followed up until 6 weeks after delivery for the occurrence of preeclampsia. The autoregulation parameter gain did not differ between pregnant and nonpregnant women. Phase was slightly but significantly higher in pregnant women, indicating better DCA. Women with a notch sign did not show altered DCA. A history of preeclampsia during a previous pregnancy was associated with lower phase in middle cerebral artery and posterior cerebral artery (P<0.05 each). During follow-up, 9 women developed preeclampsia. None of the DCA parameters were associated with the occurrence of preeclampsia. In conclusion, DCA is well preserved during late midterm pregnancy, even in women with disturbed uterine blood flow. Yet, pregnant women with preeclampsia in a previous pregnancy seem to have poorer DCA. Although limited in statistical power, this study does not support DCA as a strong early risk marker of preeclampsia.
    Hypertension 10/2013; · 6.87 Impact Factor
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    ABSTRACT: We develop nonparametric maximum likelihood estimation for the parameters of an irreversible Markov chain on states {0,1,2} from the observations with interval censored times of 0 → 1, 0 → 2 and 1 → 2 transitions. The distinguishing aspect of the data is that, in addition to all transition times being interval censored, the times of two events (0 → 1 and 1 → 2 transitions) can be censored into the same interval. This development was motivated by a common data structure in oral health research, here specifically illustrated by the data from a prospective cohort study on the longevity of dental veneers. Using the self-consistency algorithm we obtain the maximum likelihood estimators of the cumulative incidences of the times to events 1 and 2 and of the intensity of the 1 → 2 transition. This work generalizes previous results on the estimation in an "illness-death" model from interval censored observations.
    Biometrical Journal 09/2013; · 1.15 Impact Factor
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    ABSTRACT: Immunoglobulin (Ig)G cross-linking with Fc gamma receptor (FcγR)IIIB triggers neutrophil degranulation, releasing reactive oxygen species with high levels associated with protection against malaria. The FCGR3B-c.233C>A polymorphism thought to influence the interaction between IgG and FcγRIIIB was recently associated with malaria. Here, we studied the statistical interaction between glutamate rich protein antibodies and FCGR3B-c.233C>A genotypes on risk of malaria in a cohort of Ghanaian children. The absolute risk of malaria decreased more rapidly with increasing antibody levels for 233AA/AC individuals compared to 233CC children. This genotype related effect modification may significantly influence malaria sero-epidemiological and vaccine trial studies.
    The Journal of Infectious Diseases 08/2013; · 5.85 Impact Factor
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    ABSTRACT: Competing risks model time to first event and type of first event. An example from hospital epidemiology is the incidence of hospital-acquired infection, which has to account for hospital discharge of non-infected patients as a competing risk. An illness-death model would allow to further study hospital outcomes of infected patients. Such a model typically relies on a Markov assumption. However, it is conceivable that the future course of an infected patient does not only depend on the time since hospital admission and current infection status but also on the time since infection. We demonstrate how a modified competing risks model can be used for nonparametric estimation of transition probabilities when the Markov assumption is violated.
    Lifetime Data Analysis 06/2013; · 0.85 Impact Factor
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    ABSTRACT: OBJECTIVE: This study investigated whether the QTc interval on the electrocardiogram (ECG) is associated with onset of atrial fibrillation (AF). BACKGROUND: Patients with hereditary short and long QT syndromes, representing the very extremes of the QT interval, both seem to have a high prevalence of AF. METHODS: We included 281,277 individuals, corresponding to one third of the population in the greater region of Copenhagen. These individuals had a digital ECG recorded in a general practitioner's core facility from 2001-2010. Data on drug use, comorbidity, and outcomes were collected from Danish registers. RESULTS: After a median follow-up of 5.7 years, 10,766 individuals developed AF, hereof 1,467 (14%) lone AF. Having a QTc interval below 1st percentile (≤372ms) was associated with a multivariable-adjusted hazard ratio (HR) of 1.45 (95% confidence interval [CI] 1.14-1.84, P=0.002) for AF, compared with the reference group (411-419ms). From the reference group and upwards, the risk of AF increased with QTc interval duration in a dose-response manner reaching an HR of 1.44 (95% CI 1.24-1.66, P<0.001) for those having a QTc interval ≥99th percentile (≥464ms). The association with respect to longer QTc intervals was stronger for the outcome lone AF as evidenced by an HR of 2.32 (95% CI 1.52-3.54, P<0.001) for having a QTc interval ≥99th percentile (≥458ms). CONCLUSIONS: In this large ECG study, we found a J-shaped association between QTc interval duration and risk of AF. This association was strongest with respect to the development of lone AF.
    Journal of the American College of Cardiology 04/2013; · 14.09 Impact Factor
  • Jørgen Hilden, Thomas A Gerds
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    ABSTRACT: The 'integrated discrimination improvement' (IDI) and the 'net reclassification index' (NRI) are statistics proposed as measures of the incremental prognostic impact that a new biomarker will have when added to an existing prediction model for a binary outcome. By design, both measures were meant to be intuitively appropriate, and the IDI and NRI formulae do look intuitively plausible. Both have become increasingly popular. We shall argue, however, that their use is not always safe. If IDI and NRI are used to measure gain in prediction performance, then poorly calibrated models may appear advantageous, and in a simulation study, even the model that actually generates the data (and hence is the best possible model) can be improved on without adding measured information. We illustrate these shortcomings in actual cancer data as well as by Monte Carlo simulations. In these examples, we contrast IDI and NRI with the area under ROC and the Brier score. Unlike IDI and NRI, these traditional measures have the characteristic that prognostic performance cannot be accidentally or deliberately inflated. Copyright © 2013 John Wiley & Sons, Ltd.
    Statistics in Medicine 04/2013; · 2.04 Impact Factor
  • Ulla B Mogensen, Thomas A Gerds
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    ABSTRACT: Random forest is a supervised learning method that combines many classification or regression trees for prediction. Here we describe an extension of the random forest method for building event risk prediction models in survival analysis with competing risks. In case of right-censored data, the event status at the prediction horizon is unknown for some subjects. We propose to replace the censored event status by a jackknife pseudo-value, and then to apply an implementation of random forests for uncensored data. Because the pseudo-responses take on values on a continuous scale, the node variance is chosen as split criterion for growing regression trees. In a simulation study, the pseudo split criterion is compared with the Gini split criterion when the latter is applied to the uncensored event status. To investigate the resulting pseudo random forest method for building risk prediction models, we analyze it in a simulation study of predictive performance where we compare it to Cox regression and random survival forest. The method is further illustrated in two real data sets. Copyright © 2013 John Wiley & Sons, Ltd.
    Statistics in Medicine 03/2013; · 2.04 Impact Factor
  • Giuliana Cortese, Thomas A Gerds, Per K Andersen
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    ABSTRACT: Prediction of cumulative incidences is often a primary goal in clinical studies with several endpoints. We compare predictions among competing risks models with time-dependent covariates. For a series of landmark time points, we study the predictive accuracy of a multi-state regression model, where the time-dependent covariate represents an intermediate state, and two alternative landmark approaches. At each landmark time point, the prediction performance is measured as the t-year expected Brier score where pseudovalues are constructed in order to deal with right-censored event times. We apply the methods to data from a bone marrow transplant study where graft versus host disease is considered a time-dependent covariate for predicting relapse and death in remission. Copyright © 2013 John Wiley & Sons, Ltd.
    Statistics in Medicine 03/2013; · 2.04 Impact Factor
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    ABSTRACT: Regression analysis for competing risks data can be based on generalized estimating equations. For the case with right censored data, pseudo-values were proposed to solve the estimating equations. In this article we investigate robustness of the pseudo-values against violation of the assumption that the probability of not being lost to follow-up (un-censored) is independent of the covariates. Modified pseudo-values are proposed which rely on a correctly specified regression model for the censoring times. Bias and efficiency of these methods are compared in a simulation study. Further illustration of the differences is obtained in an application to bone marrow transplantation data and a corresponding sensitivity analysis.
    Lifetime Data Analysis 02/2013; · 0.85 Impact Factor
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    ABSTRACT: AimsFamily history is an established risk factor for myocardial infarction (MI), but it is not clear how this risk changes with number and gender of first-degree relatives with MI. We used the entire Danish population to examine the importance of MI in siblings and parents.Methods and resultsThis study is a retrospective nationwide register-based cohort study including registered relatives to all Danish citizens diagnosed with MI in the period 1978-2010. In the entire Danish population we identified siblings to 7552 patients with a first-time MI. The rate ratios (RR) calculated by Poisson models showed an RR of 4.30 (95% confidence interval 3.53-5.23) for siblings of a patient with MI. Children of parents with MI also showed high risk: for children of a maternal case RR 2.40 (2.20-2.60), and of a paternal case RR 1.98 (1.98-2.09), respectively; P value for gender interaction <0.0001. A paternal case with MI at an age <50 years was associated with an RR of 3.30 (2.92-3.72) while a case >50 years was associated with a risk of 1.83 (1.73-1.93). For maternal cases below and above 50 years of age the risks were 3.23 (2.56-4.10) and 2.31 (2.11-2.52), respectively.Conclusion First-degree relatives of a patient with myocardial infarction themselves have a substantial higher risk of myocardial infarction. The risk is particularly elevated when the MI case is the mother or a sibling, and when the MI case has the infarction before the age of 50 years.
    European Heart Journal 01/2013; · 14.72 Impact Factor
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    ABSTRACT: The prognostic significance of eosinophilia after myeloablative allogeneic stem cell transplantation (ASCT) remains to be established. Patients, whom developed graft-versus-host disease (cGVHD) after ASCT, were included (n = 142). Eosinophil count was analyzed at cGVHD onset. We observed no significant association between EO and the grade of cGVHD, thrombocytopenia, nor extensive skin involvement. Importantly, we observed no significant association between cGVHD with concomitant eosinophilia and long-term clinical outcomes, and subgroup analyses revealed a considerable confounding effect of ongoing steroid treatment. In conclusion, we advocate that prognostic conclusions regarding cGVHD with concomitant eosinophilia after ASCT should be interpreted with caution.
    Leukemia research 01/2013; · 2.36 Impact Factor

Publication Stats

1k Citations
263.67 Total Impact Points

Institutions

  • 2008–2014
    • University of Copenhagen
      • • Section of Biostatistics
      • • School of Dentistry
      København, Capital Region, Denmark
  • 2013
    • CUNY Graduate Center
      New York City, New York, United States
  • 2012
    • Unité Inserm U1077
      Caen, Lower Normandy, France
  • 2010
    • Erasmus MC
      • Research Group for Public Health
      Rotterdam, South Holland, Netherlands
  • 2009
    • Technical University of Denmark
      • Department of Systems Biology
      Copenhagen, Capital Region, Denmark
    • ETH Zurich
      • Institute of Integrative Biology Zurich
      Zürich, ZH, Switzerland
  • 2001–2009
    • University of Freiburg
      • Institute of Medical Biometry and Medical Informatics
      Freiburg, Baden-Württemberg, Germany
  • 2007–2008
    • New York University College of Dentistry
      New York City, New York, United States
    • New York University
      New York City, New York, United States
  • 2005–2008
    • Universitätsklinikum Freiburg
      • Department of Prosthodontics
      Freiburg, Lower Saxony, Germany
    • Universität Basel
      Bâle, Basel-City, Switzerland
  • 2004–2005
    • Nihon University
      • Department of Crown and Bridge Prosthodontics
      Edo, Tōkyō, Japan